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If each person decides not to have another child depending on the current population, then annual population increase is geometric. Each radioactive component disintegrates individually, resulting in a set decay rate that is also geometric. Geometric series are valuable because they may be used as a model for real-life circumstances. They can be employed in physics.
Geometric Progression
A geometric progression, also referred as a geometric sequence, is a non-zero numerical sequence in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio. For example, the geometric progression 2, 6, 18, 54……has a common ratio of 3. Similarly, the geometric sequence 10, 5, 2.5, 1.25…..has a common ratio of 1/2.
The value of the common ratio determines how a geometric sequence behaves.
If the standard deviation is:
- positive, all of the phrases will have the same sign as the first.
- The terms will switch back and forth between positive and negative.
- There will be exponential development towards positive or negative infinity when the number is bigger than one (depending on the sign of the initial term).
- The evolution follows a set pattern.
- There will be exponential degradation towards zero (0) between1, but not zero.
- Each term in the series has the same absolute value and terms alternate in sign.
- Due to the alternating sign, there is exponential development towards (unsigned) infinity for absolute values smaller than 1.
How is geometric progression applied in real life?
GP occurs in real life when each actor in a system behaves independently and is fixed. Examples include: If each person decides not to have another child depending on the current population, then annual population increase is geometric.
Each radioactive component disintegrates independently, resulting in a constant decay rate for each.
Interest rates, email chains, and so on are other instances. Geometric series are valuable because they may be used as a model for real-life circumstances.
Geometric sequences have a variety of applications in daily life, but one of the most prevalent is calculating interest. A term in a series is calculated by multiplying the first value in the sequence by a rate increased to the power of just less than the term number.
Applications of geometric Progression in real life
I’ll give you a handful of examples: When each person decides not to have another child based on the current population, population growth is geometric.
Use sequences in real life
Sequences are useful in both everyday life and higher mathematics. For example, sequences include the interest component of monthly payments made to pay off an automotive or home loan, as well as a month’s worth of maximum daily temperatures in one place.
Geometric progression properties
The properties of G.P are as follows:
- If each term in the G.P is multiplied or divided by a non zero amount, the new sequence is also in G.P with the same common difference.
- A G.P is formed by the reciprocal of all terms in G.P.
- The new series is already in G.P if all the terms in a G.P are increased to the same power.
- The three non-zero terms x,y and z are in G.P. if y2=xz.
Where can you apply geometric sequence?
Mathematicians use geometric series all the time. Physics, engineering, biology, economics, computer science, queueing theory, and finance all benefit from them. Geometric series are one of the simplest instances of infinite series with finite sums, albeit this trait does not apply to all of them.
Conclusion
A geometric progression is a sequence in which each subsequent element is derived by multiplying the preceding element by a constant known as the common ratio, indicated by r. For example, the geometric sequence 1, 2, 4, 8, 16, 32….. has a common ratio of r=2. The relation between the two consecutive terms in this sequence is a fixed value. Geometric Progression is the name given to such a sequence. Moreover, the geometric progression is a sequence in which the initial term is non zero and each subsequent term is generated by multiplying the previous term by a constant. The major difference between an arithmetic and a geometric sequence is that an arithmetic series has a constant difference between consecutive terms, whereas a geometric sequence has a constant ratio between successive terms.
